Why does the 90th percentile come out to be greater than the greatest number? Why is the 90th percentile of the following numbers 0.193204884?
0.193111065
0.188885706
0.191501273
0.193298704
0.18895934
0.192364606How can the 90th percentile be greater than the greatest number in the set?
I used the formula - =PERCENTILE(R:R,0.9) on excel. [R:R is the excel range which contains the following numbers]
However, the 90th perentile of 1,2,3,4,5 comes out to be 4.6 which seems correct.
 A: Comment continued. R statistical software allows you to choose from among several different definitions of quantile, all widely used. [See documentation.]
set.seed(1119)
x = sort(round(rnorm(11, 50, 5)))
x
[1] 42 43 46 47 48 51 52 52 53 55 59

Here are results for quartiles using several different types.
quantile(x, type=4)
   0%   25%   50%   75%  100% 
42.00 45.25 49.50 52.25 59.00 

quantile(x, type=5)
   0%   25%   50%   75%  100% 
42.00 46.25 51.00 52.75 59.00 

quantile(x, type=6)
  0%  25%  50%  75% 100% 
  42   46   51   53   59 

The idea is that some compromises are required when trying to partition
eleven values into four appropriate groups; also the presence of ties
can complicate finding quantiles. There is no universal agreement
how best to do this.  R uses type 7 as it's default.
quantile(x)  # if type unspecified, you get type 7
  0%  25%  50%  75% 100% 
42.0 46.5 51.0 52.5 59.0 

So don't be surprised of you encounter discrepancies between a textbook
definition and a particular type of software.
